Estimation and Inference of Treatment Effects with $L_2$-Boosting in High-Dimensional Settings
This work addresses the challenge of reliable statistical inference in high-dimensional data for empirical researchers, representing an incremental improvement by adapting boosting methods to match Lasso-like performance without strong assumptions.
The paper tackles the problem of valid inference for treatment effects after using L2-Boosting for variable selection in high-dimensional settings, establishing convergence rates similar to Lasso and extending results to 2SLS for instrumental variable models, with simulation comparisons to Lasso and an empirical application estimating bank merger effects.
Empirical researchers are increasingly faced with rich data sets containing many controls or instrumental variables, making it essential to choose an appropriate approach to variable selection. In this paper, we provide results for valid inference after post- or orthogonal $L_2$-Boosting is used for variable selection. We consider treatment effects after selecting among many control variables and instrumental variable models with potentially many instruments. To achieve this, we establish new results for the rate of convergence of iterated post-$L_2$-Boosting and orthogonal $L_2$-Boosting in a high-dimensional setting similar to Lasso, i.e., under approximate sparsity without assuming the beta-min condition. These results are extended to the 2SLS framework and valid inference is provided for treatment effect analysis. We give extensive simulation results for the proposed methods and compare them with Lasso. In an empirical application, we construct efficient IVs with our proposed methods to estimate the effect of pre-merger overlap of bank branch networks in the US on the post-merger stock returns of the acquirer bank.